Ishaan is 4 times as old as Ashley. Fifteen years ago, Ishaan was 9 times as old as Ashley. How old is Ashley now?
Answer: We can use the given information to write down two equations that describe the ages of Ishaan and Ashley. Let Ishaan's current age be $i$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $i = 4a$ Fifteen years ago, Ishaan was $i - 15$ years old, and Ashley was $a - 15$ years old. The information in the second sentence can be expressed in the following equation: $i - 15 = 9(a - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $a$ , it might be easiest to use our first equation for $i$ and substitute it into our second equation. Our first equation is: $i = 4a$ . Substituting this into our second equation, we get: $4a$ $-$ $15 = 9(a - 15)$ which combines the information about $a$ from both of our original equations. Simplifying the right side of this equation, we get: $4 a - 15 = 9 a - 135$ Solving for $a$ , we get: $5 a = 120.$ $a = 24$.